\documentclass[9pt]{article}
\usepackage{amsmath}
\begin{document}
Read in the following dictionary:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{8}   &  0.0 & -8.00 x_{1} & +  1.00 x_{2} & +  3.00 x_{3} & + 10.00 x_{4} & +  2.00 x_{5} & +  8.00 x_{6} & -4.00 x_{7}\\
 x_{9}   &  45.0 & +  2.00 x_{1} & +  8.00 x_{2} & -6.00 x_{3} & -5.00 x_{4} & +  5.00 x_{5} & -10.00 x_{6} & -8.00 x_{7}\\
 x_{10}   &  79.0 & +  6.00 x_{1} & -6.00 x_{2} & -9.00 x_{3} & +  3.00 x_{4} & -10.00 x_{5} & -3.00 x_{6} & -10.00 x_{7}\\
 x_{11}   &  1.0 & +  9.00 x_{1} & -9.00 x_{2} & +  3.00 x_{3} & -7.00 x_{4} & +  2.00 x_{5} & +  7.00 x_{6} & +  6.00 x_{7}\\
 x_{12}   &  0.0  &   & -6.00 x_{2} & -1.00 x_{3} & +  7.00 x_{4} & +  8.00 x_{5} & -8.00 x_{6} &   \\
\hline
z    &  0.0 & -5.00 x_{1} & -2.00 x_{2} & -4.00 x_{3} & -1.00 x_{4} & +  2.00 x_{5} & -2.00 x_{6} & +  4.00 x_{7}\\
\end{array}\]
No initialization required --> Proceed to Optimize. 
\section{Optimization Phase Simplex}
Starting Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{8}   &  0.0 & -8.00 x_{1} & +  1.00 x_{2} & +  3.00 x_{3} & + 10.00 x_{4} & +  2.00 x_{5} & +  8.00 x_{6} & -4.00 x_{7}\\
 x_{9}   &  45.0 & +  2.00 x_{1} & +  8.00 x_{2} & -6.00 x_{3} & -5.00 x_{4} & +  5.00 x_{5} & -10.00 x_{6} & -8.00 x_{7}\\
 x_{10}   &  79.0 & +  6.00 x_{1} & -6.00 x_{2} & -9.00 x_{3} & +  3.00 x_{4} & -10.00 x_{5} & -3.00 x_{6} & -10.00 x_{7}\\
 x_{11}   &  1.0 & +  9.00 x_{1} & -9.00 x_{2} & +  3.00 x_{3} & -7.00 x_{4} & +  2.00 x_{5} & +  7.00 x_{6} & +  6.00 x_{7}\\
 x_{12}   &  0.0  &   & -6.00 x_{2} & -1.00 x_{3} & +  7.00 x_{4} & +  8.00 x_{5} & -8.00 x_{6} &   \\
\hline
z    &  0.0 & -5.00 x_{1} & -2.00 x_{2} & -4.00 x_{3} & -1.00 x_{4} & +  2.00 x_{5} & -2.00 x_{6} & +  4.00 x_{7}\\
\end{array}\]


 $ x_{5} $ enters and $ x_{10} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{8}   &  15.8 & -6.80 x_{1} & -0.20 x_{2} & +  1.20 x_{3} & + 10.60 x_{4} & -0.20 x_{10} & +  7.40 x_{6} & -6.00 x_{7}\\
 x_{9}   &  84.5 & +  5.00 x_{1} & +  5.00 x_{2} & -10.50 x_{3} & -3.50 x_{4} & -0.50 x_{10} & -11.50 x_{6} & -13.00 x_{7}\\
 x_{5}   &  7.9 & +  0.60 x_{1} & -0.60 x_{2} & -0.90 x_{3} & +  0.30 x_{4} & -0.10 x_{10} & -0.30 x_{6} & -1.00 x_{7}\\
 x_{11}   &  16.8 & + 10.20 x_{1} & -10.20 x_{2} & +  1.20 x_{3} & -6.40 x_{4} & -0.20 x_{10} & +  6.40 x_{6} & +  4.00 x_{7}\\
 x_{12}   &  63.2 & +  4.80 x_{1} & -10.80 x_{2} & -8.20 x_{3} & +  9.40 x_{4} & -0.80 x_{10} & -10.40 x_{6} & -8.00 x_{7}\\
\hline
z    &  15.8 & -3.80 x_{1} & -3.20 x_{2} & -5.80 x_{3} & -0.40 x_{4} & -0.20 x_{10} & -2.60 x_{6} & +  2.00 x_{7}\\
\end{array}\]


 $ x_{7} $ enters and $ x_{8} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{7}   &  2.63333333333 & -1.13 x_{1} & -0.03 x_{2} & +  0.20 x_{3} & +  1.77 x_{4} & -0.03 x_{10} & +  1.23 x_{6} & -0.17 x_{8}\\
 x_{9}   &  50.2666666667 & + 19.73 x_{1} & +  5.43 x_{2} & -13.10 x_{3} & -26.47 x_{4} & -0.07 x_{10} & -27.53 x_{6} & +  2.17 x_{8}\\
 x_{5}   &  5.26666666667 & +  1.73 x_{1} & -0.57 x_{2} & -1.10 x_{3} & -1.47 x_{4} & -0.07 x_{10} & -1.53 x_{6} & +  0.17 x_{8}\\
 x_{11}   &  27.3333333333 & +  5.67 x_{1} & -10.33 x_{2} & +  2.00 x_{3} & +  0.67 x_{4} & -0.33 x_{10} & + 11.33 x_{6} & -0.67 x_{8}\\
 x_{12}   &  42.1333333333 & + 13.87 x_{1} & -10.53 x_{2} & -9.80 x_{3} & -4.73 x_{4} & -0.53 x_{10} & -20.27 x_{6} & +  1.33 x_{8}\\
\hline
z    &  21.0666666667 & -6.07 x_{1} & -3.27 x_{2} & -5.40 x_{3} & +  3.13 x_{4} & -0.27 x_{10} & -0.13 x_{6} & -0.33 x_{8}\\
\end{array}\]


 $ x_{4} $ enters and $ x_{9} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{7}   &  5.98866498741 & +  0.18 x_{1} & +  0.33 x_{2} & -0.67 x_{3} & -0.07 x_{9} & -0.04 x_{10} & -0.60 x_{6} & -0.02 x_{8}\\
 x_{4}   &  1.89924433249 & +  0.75 x_{1} & +  0.21 x_{2} & -0.49 x_{3} & -0.04 x_{9} & -0.00 x_{10} & -1.04 x_{6} & +  0.08 x_{8}\\
 x_{5}   &  2.48110831234 & +  0.64 x_{1} & -0.87 x_{2} & -0.37 x_{3} & +  0.06 x_{9} & -0.06 x_{10} & -0.01 x_{6} & +  0.05 x_{8}\\
 x_{11}   &  28.5994962217 & +  6.16 x_{1} & -10.20 x_{2} & +  1.67 x_{3} & -0.03 x_{9} & -0.34 x_{10} & + 10.64 x_{6} & -0.61 x_{8}\\
 x_{12}   &  33.1435768262 & + 10.34 x_{1} & -11.51 x_{2} & -7.46 x_{3} & +  0.18 x_{9} & -0.52 x_{10} & -15.34 x_{6} & +  0.95 x_{8}\\
\hline
z    &  27.0176322418 & -3.73 x_{1} & -2.62 x_{2} & -6.95 x_{3} & -0.12 x_{9} & -0.27 x_{10} & -3.39 x_{6} & -0.08 x_{8}\\
\end{array}\]
Final Dictionary
Solution:  27.0176322418
Num Pivots:  4
\end{document}
